We consider the problem of dynamically indexing temporal observations about a collection of objects, each observation consisting of a key identifying the object, a list of attribute values and a timestamp indicating the time at which these values were recorded. We make no assumptions about the rates at which these observations are collected, nor do we assume that the various objects have about the same number of observations. We develop indexing structures that are almost linear in the total number of observations available at any given time instance, and that support dynamic additions of new observations in polylogarithmic time. Moreover, these structures allow the quick handling of queries to identify objects whose attribute values fall within a certain range at every time instance of a specified time interval. Provably good bounds are established.